If you spot a £10 note on the pavement, it's a fake – or else someone would have picked it up already. That is the insight of the "efficient market" school of economics, which was the rage until the 2007-08 crunch raised niggling doubts about whether every financial trade truly did have to take rational account of every last bit of available information. Given the unfolding scandal gripping the City, it seems more pertinent to say that if you spot a banknote sticking out of someone's pocket then your eyes are deceiving you – or else somebody else would have pinched it.

The details of Barclays' interest rate-rigging will be lost on the majority of Britons, who know not what Libor stands for and have less idea how it tracks back to their own pockets. Asking bankers to rate their own risks may have been like asking tobacco manufacturers to write the health warnings, but the calculation of interbank lending costs will remain a minority sport. The point of principle, however, is stark – and it is more lie than bore. Four years ago Lehman toppled, and society learned that complex derivatives that were supposed to spread risk around efficiently instead concentrated it catastrophically. If that was a figurative fraud, something closer to a literal one is now being uncovered. Bankers said untrue things about the price they would have to pay to borrow money, with a view to reaffirming the hardy reputation of an institution which was energetically stuffing their pockets.

This deception was apparently systematic, and principally within the Barclays Capital arm that Bob Diamond ran until last year. The unembarrassable Mr Diamond is now trying to hang on as chief executive of Barclays as a whole. Monday's resignation of the chairman, Marcus Agius, aimed to deflect the rage. But the chair has neither the responsibility nor the direct powers to shake up a company's culture; the chief executive has both. In parliamentary committees this week we may glean more about who knew what when, but it would be extraordinary if Mr Agius knew more than the CEO himself; the expectation would be the reverse. Ignorance about operations for which one is responsible for is a woeful defence, and even if Mr Diamond can demonstrate that loftier concerns led him to take his eyes off his underlings, he will have grave difficulty in fulfilling his promise to staff yesterday, to restore his bank's battered reputation. His remaining plea in mitigation is other banks were at it too.

That is very likely. Manipulating a statistical average, such as Libor, would be easier in corporate concert than in isolation, and it is understood at least 16 other banks are being investigated. This wider canvas makes the case for the most sweeping of inquiries. David Cameron yesterday announced a probe by a committee of MPs and peers, arguing for something brisk over something more thorough, on the lines of the Leveson inquiry. A little later the chancellor unveiled the detail and taunted his Labour shadow, Ed Balls, for having been a laissez-faire City minister; Mr Balls retorted that Mr Osborne was forever demanding a still-lighter touch back then. Such backward-looking and partisan bickering will likely prevent parliamentarians from providing the dispassionate analysis required. Lord Justice Leveson's hearings offer a more promising model for a wider probe which could also grapple with many banks' (and especially Barclays') long record of legal tax avoidance.

Both the main parties fell under the spell of the bankers. New Labour invited them into government to advise on things like the NHS, and manage "a public portfolio", which included everything from the canals to the Royal Mail. Even after their magic was exposed as alchemy in 2008, they retained great sway which survived the change in administration in 2010. To see that just look at the watering down of several important recommendations of the Vickers commission after lobbying.

We now know the banks' tricks involved not just dubious wizardry but a measure of wickedness too. That surely gives a final chance to break the spell – it is a chance which must be seized, through a proper judge-led inquiry.